Vacuum densities and the Casimir forces for branes orthogonal to the AdS boundary

Bellucci, Stefano; Saharian, A. A.; Kotanjyan, V. Kh.

doi:10.1103/physrevd.106.065021

Cited by 2 publications

(5 citation statements)

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“…In order to evaluate the corresponding VEV, the Hadamard function is used, obtained from the positive frequency Wightman function from Ref. [56]. In the region between the branes, the Hadamard function is decomposed into single-brane and the second-braneinduced contributions.…”

Section: Discussionmentioning

confidence: 99%

“…For the scalar field modes in the region between the branes, the eigenvalues of the quantum number k 1 , corresponding to the momentum along the direction x 1 , are quantized by the boundary conditions (4). Those eigenvalues are roots of the transcendental equation (see [56])…”

Section: Geometry Of the Problemmentioning

confidence: 99%

“…The expression for the Hadamard function in the region between the branes is obtained from the corresponding expression for the Wightman function derived in Ref. [56]. The Wightman function is presented in the decomposed form…”

Section: General Expressionmentioning

confidence: 99%

“…Motivated by those developments, the influence of branes orthogonally intersecting the AdS boundary on the local properties of the scalar vacuum in a general number of spatial dimensions was studied in Refs. [55,56]. As local characteristics of the vacuum state, the expectation values of the field squared and of the energy-momentum tensor were considered.…”

Section: Introductionmentioning

confidence: 99%

“…Section 2 describes the geometry of the problem and present the expression for the surface energy-momentum tensor. The corresponding vacuum expectation value (VEV) is investigated in Section 3 by using the two-point function from [56]. The surface energy density is decomposed into contributions corresponding to the self-energy of the brane when the second brane is absent and the part induced by the second brane.…”

Section: Introductionmentioning

confidence: 99%

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Surface Casimir Densities on Branes Orthogonal to the Boundary of Anti-De Sitter Spacetime

Saharian

2023

Physics

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The paper investigates the vacuum expectation value of the surface energy–momentum tensor (SEMT) for a scalar field with general curvature coupling in the geometry of two branes orthogonal to the boundary of anti-de Sitter (AdS) spacetime. For Robin boundary conditions on the branes, the SEMT is decomposed into the contributions corresponding to the self-energies of the branes and the parts induced by the presence of the second brane. The renormalization is required for the first parts only, and for the corresponding regularization the generalized zeta function method is employed. The induced SEMT is finite and is free from renormalization ambiguities. For an observer living on the brane, the corresponding equation of state is of the cosmological constant type. Depending on the boundary conditions and on the separation between the branes, the surface energy densities can be either positive or negative. The energy density induced on the brane vanishes in special cases of Dirichlet and Neumann boundary conditions on that brane. The effect of gravity on the induced SEMT is essential at separations between the branes of the order or larger than the curvature radius for AdS spacetime. In the considerably large separation limit, the decay of the SEMT, as a function of the proper separation, follows a power law for both massless and massive fields. For parallel plates in Minkowski bulk and for massive fields the fall-off of the corresponding expectation value is exponential.

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Section: Discussionmentioning

confidence: 99%

Section: Geometry Of the Problemmentioning

confidence: 99%

Section: General Expressionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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